1. Field of the Invention
The present invention relates to the field of digital transmission of data and more particularly to a process for modulation and for determining the bit loading on a communication channel.
2. Description of the Related Art
As communication networks are constantly developing, techniques of modulation need to be more and more effective so as to increase the data rate of the communications.
FIG. 1A illustrates the transmission of a digital signal Xi through a Additive White Gaussian Noise (AWGN) channel. In this situation, the input signal xi undergoes the effect of a complex gain Hi associated to a white noise ni of variance Ni.yi=Hi xi+ni
The input signal xi is defined in accordance with the modulation scheme retained. It belongs to a predefined set—or constellation—of complex numbers. In the so-called Binary Phase Shift Keying (B.P.S.K.) modulation, the constellation comprises the two values, −1 and +1 respectively and, in a four states Quadrature Amplitude Modulation or 4QAM such as illustrated in FIG. 1B—the constellation comprises a set of four complex points.
The modulation of the signal to be transmitted requires an operation known as labeling or mapping, which comprises the establishment of a direct and unique relation between the signal composed of symbols or words which are to be transmitted and the different points forming the constellation. In a 4QAM modulation, four 2-bit words are associated to each point of the constellation so as two bits can be simultaneously transmitted through the communication channel.
For static or quasi-statics transmission channels, the choice of the constellation—and thus the number of bits simultaneously transmitted on the channel—is chosen as a function of the characteristics of the channel which are measured, generally before the start of the transmission, by a direct measure of the signal to noise ratio after the establishment of the channel. The number of bits which can be loaded on the channel—or the order or size of the constellation—is set to a high value when the signal to noise ratio shows to be favorable. In practice, the size of the constellation is determined as a function of the characteristics of the channel, assumed static or quasi-static—derived from the measurement of the received signal to noise ratio measured in reception and returned to the emitter before the start of the transmission so as to set the order of the constellation. In a Orthogonal Frequency Duplex Modulation (OFDM) or Discrete Multi-Tone (DMT) communication system, a number of subcarriers are associated and different signals can be added, each signal being translated to one particular frequency or subcarrier. The size of the constellation is set in accordance with the response of the channel for the particular frequency of the subcarrier which is considered. Thus the subcarrier with the more favorable signal to noise ratio will be associated to a constellation of high size—up to fifteen bits which are parallely transmitted—while the less favorable subcarriers will correspond to low size constellations.
To one constellation will correspond a number of bits which are simultaneously transmitted through the channel. A digital transmission system—as known in the art—will use a constellation with a given s corresponding bitloading—which is determined for each subcarrier. In practice, for each channel (or subcarrier), there is determined the higher size of the constellation which, for a standardized emission power of 1, provides with an error bit rate below to a given threshold, for instance 10−4. The bitloading then derives from the constellation.
The following formula is known for determining the number of bits to use for one subcarrier in the case where no error correcting technique is used:
  b  =                    log                                                  ⁢          2                    ⁡              (        M        )              =                  log                                                  ⁢          2                    ⁡              (                  1          +                                    SNR              out                        Γ                          )            
with
      SNR    out    =                                      H          i                            2              N      i      being the signal to noise ratio at the output of the channel, and Γ corresponding to a performance level representative of the probability Pbit that an error occurs in reception. Briefly, in accordance with this value Γ and also the signal to noise ratio SNRout, the size of the constellation can be precisely adjusted, and therefore the bitloading for the considered channel.
Thus, the bitloading is classically determined by the measurement of the signal to noise ratio in reception. If this determination shows to be satisfactory for transmission systems without error correcting technique, the determination is much more complex when an error correcting code is introduced within the modulation scheme, such as a Reed-Solomon code for instance. In that case, the symbols which are uniquely associated to the points of the constellation by means of the labeling operation do no longer consist in unpredictable information, but also comprises redundant information which depends on the error correcting coded utilized.
The computation of the size of the constellation to utilize—and therefore the bitloading within the channel—is clearly more difficult. This problem is usually solved by means of an intermediary calculation, based on the use of a coding gain resulting from the error correcting code. This permits to reduce the problem to the theoretical and ideal situation of a modulation without coding so as to take advantage of the existing formulas for determining the constellation and computing the bitloading. For an bit error rate of 10−7 for instance with coding, the corresponding bit error rate without coder is computed, for instance 10−4, and the last value is then used for determined the appropriate constellation as well as the bitloading on the channel.
As can be seen, this computation—although widely used in the art—is clearly an empirical approach which prevents precision in the determination of the constellation. More generally, modulation systems using error correcting codes do not easily permit the determination of the bit loading.
There is a need for a new structure of modulator which fits the use of error correcting code and which still permits the determination of the bitloading to be used in one or more transmission channels. Particularly, it is desirable to achieve a new algorithm which achieves the determination of the constellation to utilize and which is adapted to the use of an error correcting code.